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Proof step 15 from proof RED-correct (previous step)

〈RED1(t; tn0)〉 tn0 = some(t3), 〈RED1(t; tn0): kappa0 〉 tn0 = some(t3), 〈RED(t3; t0): kappa0 〉 t0 = t1, t => t3, ¬ t =>* t1, t3 =>* t1, irred(t1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ t =>* t' ↔ (∃ n. (=> ^ n)(t, t'))
Proof step 14:
〈RED(t3; t0): kappa0 〉 t0 = t1, 〈RED1(t; tn0): kappa0 〉 tn0 = some(t3), 〈RED1(t; tn0)〉 tn0 = some(t3), t => t3, ¬ t =>* t1, ∃ n. (=> ^ n)(t3, t1), irred(t1) ⊦

Rule argument

[x0lemmaarg: spec-name: reduce instance-name: lemma-name: reduce-def antecedent: succedent: t =>* t' ↔ (∃ n. (=> ^ n)(t, t')) substlist: [t', t] → [t1, t3] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 5)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t1, t3)]]